Comparing the R algorithm and RHMC for staggered fermions

TL;DR

This paper compares the R algorithm and RHMC for simulating staggered fermions, analyzing their accuracy and proposing RHMC as an exact alternative to test the R algorithm's validity.

Contribution

It provides a proof of the R algorithm's convergence rate and introduces RHMC as an exact method to validate R algorithm simulations.

Findings

R algorithm converges with O(dt^2) errors, dependent on (dt/m)^2

RHMC offers an exact alternative without step size errors

Proposes using RHMC to test R algorithm validity in practical simulations

Abstract

The R algorithm is widely used for simulating two flavours of dynamical staggered fermions. We give a simple proof that the algorithm converges to the desired probability distribution to within O(dt^2) errors, but show that the relevant expansion parameter is (dt/m)^2, m being the quark mass. The Rational Hybrid Monte Carlo (RHMC) algorithm provides an exact (i.e., has no step size errors) alternative for simulating the square root of the staggered Dirac operator. We propose using it to test the validity of the R algorithm for simulations carried out with dt m.